On a nonlinear Kalman filter with simplified divided difference approximation
We present a new ensemble-based approach that handles nonlinearity based on a simplified divided difference approximation through Stirling's interpolation formula, which is hence called the simplified divided difference filter (sDDF). The sDDF uses Stirling's interpolation formula to evalu...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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2012
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| _version_ | 1797105102536835072 |
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| author | Luo, X Hoteit, I Moroz, I |
| author_facet | Luo, X Hoteit, I Moroz, I |
| author_sort | Luo, X |
| collection | OXFORD |
| description | We present a new ensemble-based approach that handles nonlinearity based on a simplified divided difference approximation through Stirling's interpolation formula, which is hence called the simplified divided difference filter (sDDF). The sDDF uses Stirling's interpolation formula to evaluate the statistics of the background ensemble during the prediction step, while at the filtering step the sDDF employs the formulae in an ensemble square root filter (EnSRF) to update the background to the analysis. In this sense, the sDDF is a hybrid of Stirling's interpolation formula and the EnSRF method, while the computational cost of the sDDF is less than that of the EnSRF. Numerical comparison between the sDDF and the EnSRF, with the ensemble transform Kalman filter (ETKF) as the representative, is conducted. The experiment results suggest that the sDDF outperforms the ETKF with a relatively large ensemble size, and thus is a good candidate for data assimilation in systems with moderate dimensions. © 2011 Elsevier B.V. All rights reserved. |
| first_indexed | 2024-03-07T06:42:44Z |
| format | Journal article |
| id | oxford-uuid:f9d56dc3-b5b8-4d7b-9df2-139d0d6fab77 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:42:44Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:f9d56dc3-b5b8-4d7b-9df2-139d0d6fab772022-03-27T13:01:02ZOn a nonlinear Kalman filter with simplified divided difference approximationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f9d56dc3-b5b8-4d7b-9df2-139d0d6fab77EnglishSymplectic Elements at Oxford2012Luo, XHoteit, IMoroz, IWe present a new ensemble-based approach that handles nonlinearity based on a simplified divided difference approximation through Stirling's interpolation formula, which is hence called the simplified divided difference filter (sDDF). The sDDF uses Stirling's interpolation formula to evaluate the statistics of the background ensemble during the prediction step, while at the filtering step the sDDF employs the formulae in an ensemble square root filter (EnSRF) to update the background to the analysis. In this sense, the sDDF is a hybrid of Stirling's interpolation formula and the EnSRF method, while the computational cost of the sDDF is less than that of the EnSRF. Numerical comparison between the sDDF and the EnSRF, with the ensemble transform Kalman filter (ETKF) as the representative, is conducted. The experiment results suggest that the sDDF outperforms the ETKF with a relatively large ensemble size, and thus is a good candidate for data assimilation in systems with moderate dimensions. © 2011 Elsevier B.V. All rights reserved. |
| spellingShingle | Luo, X Hoteit, I Moroz, I On a nonlinear Kalman filter with simplified divided difference approximation |
| title | On a nonlinear Kalman filter with simplified divided difference approximation |
| title_full | On a nonlinear Kalman filter with simplified divided difference approximation |
| title_fullStr | On a nonlinear Kalman filter with simplified divided difference approximation |
| title_full_unstemmed | On a nonlinear Kalman filter with simplified divided difference approximation |
| title_short | On a nonlinear Kalman filter with simplified divided difference approximation |
| title_sort | on a nonlinear kalman filter with simplified divided difference approximation |
| work_keys_str_mv | AT luox onanonlinearkalmanfilterwithsimplifieddivideddifferenceapproximation AT hoteiti onanonlinearkalmanfilterwithsimplifieddivideddifferenceapproximation AT morozi onanonlinearkalmanfilterwithsimplifieddivideddifferenceapproximation |